What is the solution for 2*(d^2y)/(dx^2)-5(dy)/(dx)-3y=0 ?

The solution for 2*(d^2y)/(dx^2)-5(dy)/(dx)-3y=0 is y=c_{1}e^{3x}+c_{2}e^{-x/2}

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2*(d^2y)/(dx^2)-5(dy)/(dx)-3y=0

2 \cdot \frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 3 y = 0

y = c_{1} e^{3 x} + c_{2} e^{- \frac{x}{2}}

Solution steps

2 \cdot \frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 3 y = 0

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- \frac{x}{2}}

y = c_{1} e^{3 x} + c_{2} e^{- \frac{x}{2}}

u^{^{''}} + 2 r u^{^{'}} (t) + a H (t) = 0

16 y^{^{''}} - y = 0, y (- 4) = 1, y^{^{'}} (- 4) = - 1

y^{^{''}} + 16 y^{^{'}} + 64 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} = 0, y (0) = 6 - 6 e^{4}, y (1) = 0

y^{^{'''}} - 2 y^{^{''}} + y = 0

What is the solution for 2*(d^2y)/(dx^2)-5(dy)/(dx)-3y=0 ?
The solution for 2*(d^2y)/(dx^2)-5(dy)/(dx)-3y=0 is y=c_{1}e^{3x}+c_{2}e^{-x/2}